Question: Determine the intercepts of the line. $ y=-3x+12$ $y$ -intercept: $\Big($
Explanation: The $y$ -intercept of a graph is the point of intersection between the $y$ -axis and the graph. Since the $y$ -axis is also the line $x=0$, the $x$ -value of this point will always be $0$. The $x$ -intercept of a graph is the point of intersection between the $x$ -axis and the graph. Since the $x$ -axis is also the line $y=0$, the $y$ -value of this point will always be $0$. To find the $y$ -intercept, let's substitute $ x= 0$ into the equation and solve for $y$ : $\begin{aligned}y&=-3\cdot{0}+12\\ y&=12\end{aligned}$ So the $y$ -intercept is $\left(0,12\right)$. Generally, in linear equations of the form $y=m\!\!\,\cdot\!\!x+b$ (which is called slope-intercept form ), the $y$ -intercept is $(0,b)$. To find the $x$ -intercept, let's substitute $ y= 0$ into the equation and solve for $x$ : $\begin{aligned}{0}&=-3x+12\\ 3x&=12\\ x&=4\end{aligned}$ So the $x$ -intercept is $\left(4,0\right)$. In conclusion, The $y$ -intercept is $\left(0,12\right)$. The $x$ -intercept is $\left(4,0\right)$.